Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years. They both purchased new cars this year. When will they next both purchase new cars in the same year? A. in 2 years B. in 8 years C. in 12 years D. in 24 years

Question

Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years. They both purchased new cars this year. When will they next both purchase new cars in the same year? A. in 2 years B. in 8 years C. in 12 years D. in 24 years

Answer 1

To find the next year they will both purchase new cars, we need to find the least common multiple (LCM) of 4 and 6.

Prime factorization of 4: 2 * 2
Prime factorization of 6: 2 * 3

Multiplying the highest powers of all prime factors together gives the LCM: 2 * 2 * 3 = 12

Therefore, they will next purchase new cars in the same year in 12 years.

So the correct answer is C. in 12 years.